Quantum cosmology with big-brake singularity

TL;DR

This paper explores quantum cosmological models with a big-brake singularity, demonstrating that quantum effects can prevent the classical singularity in both Wheeler-DeWitt and loop quantum cosmology frameworks.

Contribution

It formulates and solves the Wheeler-DeWitt equation for a big-brake singularity and compares singularity avoidance in both Wheeler-DeWitt and loop quantum cosmology.

Findings

Wave packets vanish at the classical singularity, indicating quantum avoidance.

Both Wheeler-DeWitt and loop quantum cosmology models avoid the big-brake singularity.

Quantum effects modify the classical singular behavior in the models.

Abstract

We investigate a cosmological model with a big-brake singularity in the future: while the first time derivative of the scale factor goes to zero, its second time derivative tends to minus infinity. Although we also discuss the classical version of the model in some detail, our main interest lies in its quantization. We formulate the Wheeler-DeWitt equation and derive solutions describing wave packets. We show that all such solutions vanish in the region of the classical singularity, a behaviour which we interpret as singularity avoidance. We then discuss the same situation in loop quantum cosmology. While this leads to a different factor ordering, the singularity is there avoided, too.